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From 𝞶 < 108 Hz to 𝞶 > 1028 Hz
The electromagnetic spectrum
Conversion to temperature in case of equilibrium radiation-matter (L. Boltzmann: motion of particles relates to its temperature)
Sensitivity of human eye from 390 nm to 780 nm
– 1 –
E =h c
�= h ⌫ (1)
EK ⇠ k T (2)
Constants:
c = 299, 792 km s�1
h = 6.626⇥ 10�34
J s = 6.626⇥ 10�27
erg s = 4.136⇥ 10�15
eV s
k = 1.381⇥ 10�23
JK�1
= 1.381⇥ 10�16
erg K�1
Conversions:
1 J = 1⇥ 107erg
1 eV = 1.602⇥ 10�12
erg
1 eV = 2.418⇥ 1014Hz = 2.418⇥ 10
5GHz
1 eV = 1.160⇥ 104K
1 eV ! 1.240⇥ 10�6
m = 1.240µm
Energy of a single photon (and conversion units)
Energy of photon with wavelength λ or frequency ν
Light speed
Planck constant
Boltzmann constant
Kinetic energy of gas at temperature T
(k : Boltzmann constant)
Reference table
Need a combination of ground-based and satellite observations
log ν
50km
100km
X-Rays Gamma-RaysInfrared Radiation
Radio- Waves
UV
Rad
iatio
n
Opt
ical
Lig
ht
Abs
orpt
ion
Ban
ds d
ue to
O3,
N, O
CO2,H2O,O3...
Ref
lect
ion
10km
log λ
Microwave / Sub-millimeter
Observational windows of electromagnetic radiation
Measuring distances
Trigonometric parallax
b
d = b/sin( p) ≈ b/pvalid for small p (always valid for stars) and p measured in radians
b : 150 million km = 1 Astronomical Unit (AU)
Definition of 1 parsec: distance d for p = 1 arcsec 1 parsec = 3.2558 light years
The Big Dipper
Alkaloid (210 light years)
Megrez (63 light years)
The Big Dipper
Measuring radial velocity of stars
Doppler shift: shift of observed wavelength in distant sources due to motion with respect to Earth
Absorption lines of the hydrogen atom
Wavelength
Used to measure radial velocity of stars with respect to Earth
Energy levels of the hydrogen atom(the most abundant in the universe)
Ionisation level
Ground level
Binary stars, multiple systems, star clusters
A
BSiriusBrightest star in the night skyMagnitude: mV = −1.5Distance from Earth: 2.64 pcBinary system A & BRotation period: 50 yearsSeparation between stars: 8.2 to 31.5 AU
Close binary systems used to estimate mass of stars
Binary systems discovered with one star occulting other stareclipsing binary systems
AB AB
A B A
Pleiades (or Seven Sisters)Open star cluster (over 1000 stars)Distance: 136.2 ± 1.2 pcRadius: ~ 8 l.y.
Open star clusters contain hundreds of stars
NGC 2244Distance: 1.6 kpc
Open star clusters contain hundreds of stars
NGC 6093 Distance: 10 kpcSize: 29 pc
Hubble Space Telescope (HST) image
Globular clustersMany thousands stars Spherically distributed In small volumeRotating around galaxies
Star size
Orion Constellation
BetelgeuseDistance: 197 pc
Rigel
Distance: 264 pc
Orion NebulaDistance: 412 pc
Betelgeuse Distance: 197±45 pc (640 l.y.)Magnitude: mV = 0.50Apparent size: 0.043 − 0.056 arc-secondsReal size: R ~ 1000 R⊙Image from Hubble Space Telescope
Sun
Rigel
Betelgeuse
Comparing sizes of stars (images are not real)
Massa: 1 M⊙
19 M⊙
15−20 M⊙
Angular resolution: capability to discern details of image
Low resolution High resolution
It depends on:1. Smoothness of telescope’s mirrors2. Diameter of primary mirror3. Wavelength of radiation4. Turbulence of Earth’s atmosphere
Angular resolution: smallest angle discerned in image
The atmosphere distortion of light
The atmosphere distortion of light
Ground observations Hubble Space Telescope image
Ground observations vs. Space observations
White dwarf star
Globular cluster Messier 4
Radio telescopes work with large wavelength ⟾ Low image resolution
Solution: using interferometry to improve resolution
Image resolution of telescopes θ (in radians):
λ: wavelength of electromagnetic radiationD: diameter of telescope’s mirror or antenna’s aperture
Large θ means low resolution
This is the highest possible resolution (diffraction limit)
Radio telescope design
Image angular resolution is worse for bigger θ (in radians):
λ: wavelength of electromagnetic radiationD: diameter of telescope or antenna’s aperture
Green Bank Telescope (West Virginia - USA)
Resolution is worse for radio telescopes, and better for larger D But there’s a way to improve it: interferometry
Diameter of Antenna: D = 100 m
Effective angolar resolution:
Effective diameter D
Fringe pattern is created if separation between two antennas is > 10 × λ
Virtual giant antenna
Interferometry with relatively small radio antennas to get resolution of giant telescope
Real small antennas
Formation of fringes in a Michelson interferometer
Interference patter from identical source S: superposition of electromagnetic waves
Same source ⟾ signal perfectly in phase & same frequency
Wave-f
ronts
from
distan
t sou
rce
φ
δl
baseline D
Interferometer: signal is combined from two or more telescopes to produce a sharper imageto obtain higher angular resolution
Interferometry for radio telescopes
Signal time delay: τg = δl/c c: speed of light
Atomic clock to introduce time delay τg, thencombined signals are perfectly synchronised
D cos φ = τgc
The atmospheric distortion: astronomical seeingAstronomical seeing: blurring of image due to mixing of air with different temperatures (turbulence)
Poor seeingGood seeing
Images of binary stars
At the telescope
Acquired images
More here: http://www.atnf.csiro.au/outreach/education/senior/astrophysics/atmosphere.html
Stars: temperature and luminosity
Definition of luminosity: energy emitted in electromagnetic radiation by the object per unit time (power)
Proxima CentauriDistance: 4.24 light yearsApparent magnitude: 11.13Temperature on surface: 3000 K
Surface temperature measured from spectrum of star
Modern telescopes don’t use a prism but a diffraction grating
Schematic view of a spectrograph
Spectrum of solar radiation (as seen from Earth) Approximation: Black Body spectrum
Irradiance: power of electromagnetic radiation per unit area (radiative flux) incident on a surface
Black Body (or Planck) spectrum
Wien’s displacement law: λpeak = 2.8977×10-3/T [m/K]
Black Body radiation:
Wien’s displacement law: Constant: b = 2.8977×10−3 K m
Stefan-Boltzmann law (total energy emitted by BB per unit area & time):
Low energy (Reyleigh-Jean’s law)
High energy (Wien’s law)
Approximations:
Spectral classification of stars
M0 star (3500 K).
O5 star (40,000 K)
Near infraredUltra violet
Tem
pera
ture
& m
ass
Tim
e of
hyd
roge
n bu
rnin
g
Temperature
O 30000 − 60000 K Blue stars
B 10000 − 30000 K Blue-white stars
A 7500 − 10000 K White stars
F 6000 − 7500 K Yellow-white stars
G 5000 − 6000 K Yellow stars (like the Sun - G2)
K 3500 − 5000K Yellow-orange stars
M 2600 − 3500 K Red stars
L < 2600 K
Star classification and surface temperature
Stars: magnitude and color
Response curve of human eye and telescope instruments (filters)
Solar black-body peak emission
Filters: U, B, V
Tem
pera
ture
& m
ass
Color of stars from O star to M star:−0.4 < (mB − mV ) < 1.5
(magnitude difference in B &V bands)
B Spectral classification of stars
M0 star (T = 3500 K)
O5 star (T = 40,000 K)
Near infraredUltra violet
V
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